Sufficient Conditions on the Existence of Switching Observers for Nonlinear Time-Varying Systems

We derive sufficient conditions for the solvability of the observer design problem for a wide class of nonlinear time-varying systems, including those having triangular structure. We establish that, under weaker assumptions than those imposed in the existing works in the literature, it is possible to construct a switching sequence of time-varying noncausal dynamics, exhibiting the state determination of our system.

💡 Research Summary

The paper addresses the observer design problem (ODP) for a broad class of nonlinear time‑varying systems, including those with a triangular structure. Traditional results in the literature typically rely on strong assumptions such as global Lipschitz continuity, uniform observability, or the existence of a globally defined Lyapunov function. The authors propose a substantially weaker set of conditions and demonstrate that, under these relaxed hypotheses, one can construct a sequence of time‑varying, possibly non‑causal dynamics that switch over time and still guarantee asymptotic state reconstruction.

Problem formulation and terminology
The system under consideration is written as
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